Graph search and variable neighborhood search for finding constrained longest common subsequences in artificial and real gene sequences

We consider the constrained longest common subsequence problem with an arbitrary set of input strings as well pattern strings. This has applications, for example, in computational biology where it serves a measure similarity sets molecules putative structures common. contribute several ways. First, is formally proven that finding feasible solution length is, general, NP-complete. Second, we propose heuristic approaches: greedy algorithm, beam search aiming feasibility, variable neighborhood search, and hybrid latter two approaches. An exhaustive experimental study shows effectivity differences proposed approaches respect to solution, high-quality solutions, runtime both, artificial real-world instance sets. The ones are generated from 12681 bacteria 16S rRNA gene sequences 15 primer contigs